The mathematical content covered by these measures is described under about our measures. You should be sure to check to make sure that the topics included in your research study align with with mathematical content we cover.

Next, you should think about whether your program can make good use of these measures. These measures are best suited for investigating:

• How knowledge of mathematics for teaching corresponds to other constructs, such as instructional practice, attitude toward teaching mathematics, etc.
• How knowledge of mathematics for teaching develops. Within this category, these measures are not suited to all programs, however. Instead, they are best used with:


• Programs that intend to broadly improve teachers’ knowledge in any of the content areas named above; programs which focus only on narrow bands of the K-8 math curriculum (e.g., programs which focus only on linear functions) will not likely see positive results. Programs which target significant resources at improving teachers’ knowledge—not 2-3 hours of professional development, but sustained, serious mathematical work.
• Programs that work to improve teachers’ mathematical reasoning and analysis skills.
• Programs with pre-existing curricula. Programs without pre-existing curricula—for instance, professional development where teachers can choose their own topics for investigation—complicate the design of evaluations with these measures.
• Programs with sufficient sample size to make general statements about differences between groups or over time.

Bear in mind that there are other useful ways to assess teacher knowledge growth in mathematics – for instance, via discourse analysis, interviews, or traditional end-of-course assessments. Potential users should expect the process of obtaining our measures to take three to six months, depending upon when the next training session is scheduled.

When should projects elect NOT to use these measures?

These measures are not appropriate for all research and evaluation efforts. Reasons for not using these measures include:

• Length. Typically, between 12-25 items are required to achieve reliabilities of between .7 and .8 for each scale. Teachers complete roughly one item per minute. Users who want to gauge teacher knowledge growth in diverse areas of the K-8 curriculum (e.g., geometry, algebra, number and operation) may need multiple scales in order to assess such growth.
• Alignment with your curriculum, questions, or study. Our measures were written to provide an accurate picture of teachers’ overall ability to solve mathematics problems that arise in classrooms within each of the constructs listed above. They were not written to align with any particular professional preparation program or research question. For this reason, they may not be sensitive to the actual content of your program. These measures are also not appropriate for the evaluation of programs where improving teachers’ mathematical knowledge for teaching is not a primary focus.
• Complex analyses. Instruments which carry our measures can be more difficult to design and analyze than traditional surveys.
• Small sample size. These measures were not designed or validate to make statements about any individual teacher’s level of mathematics knowledge. Instead, one might use the measures to make statements about how content knowledge differs among groups of teachers, or how a group of teachers performs at one or more time points. Usually, 60 teachers per group – or 60 teachers over time – will be adequate for comparison purposes. Effects may be found with smaller groups, but the risk of insufficient statistical power rises as group size diminishes.
• Highly knowledgeable teachers. Our measures are not well-suited to studies investigating learning among already highly knowledgeable teachers.
• Inappropriate usage. These measures cannot be used to evaluate individual teachers for tenure, pay, hiring, or any other use with high-stakes consequence. They have not been validated for this purpose.
• Non-K-8 teacher populations.These items were piloted with K-8 teachers; the joint AERA/APA Standards recommend re-piloting before use with other populations.